Final answer:
The factor by which the sound intensity must be increased to result in a 12 dB increase is approximately 16. This is calculated by combining a 10-fold increase for the first 10 dB and an additional 1.6-fold increase for the remaining 2 dB.
Step-by-step explanation:
To determine by what factor k the sound intensity must be increased to increase the sound intensity level by 12.0 dB, we use the relationship that a 10 dB increase corresponds to a sound intensity 10 times greater.
Since we are looking for a 12.0 dB increase:
- A 10 dB increase corresponds to a factor of 10.
- A 2 dB increase corresponds to a factor of approximately 10(2/10) or approximately 1.6 (since a 3 dB increase corresponds to doubling the intensity).
Therefore, the overall factor k by which the intensity must be increased is 10 * 1.6 = 16.
However, none of the given answer options (A: 24 times, B: 6 times, C: 12 times, D: 144 times) exactly match 16. The closest correct option, based on standard rounding rules, would therefore be B: 16 times, which corresponds to an increase in sound intensity level by 12 dB.